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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,lambda,z] > Identities > Recurrence identities > Distant neighbors > With respect to nu





http://functions.wolfram.com/07.14.17.0010.01









  


  










Input Form





GegenbauerC[\[Nu], \[Lambda], z] == Subscript[\[ScriptCapitalC], n][\[Nu], \[Lambda], z] GegenbauerC[\[Nu] + n, \[Lambda], z] - ((n + 1 + \[Nu])/(n - 1 + 2 \[Lambda] + \[Nu])) Subscript[\[ScriptCapitalC], n - 1][\[Nu], \[Lambda], z] GegenbauerC[\[Nu] + n + 1, \[Lambda], z] /; Subscript[\[ScriptCapitalC], 0][\[Nu], \[Lambda], z] == 1 && Subscript[\[ScriptCapitalC], 1][\[Nu], \[Lambda], z] == (2 (\[Lambda] + \[Nu] + 1) z)/(2 \[Lambda] + \[Nu]) && Subscript[\[ScriptCapitalC], n][\[Nu], \[Lambda], z] == ((2 z (n + \[Lambda] + \[Nu]))/(n - 1 + 2 \[Lambda] + \[Nu])) Subscript[\[ScriptCapitalC], n - 1][\[Nu], \[Lambda], z] - ((\[Nu] + n)/(n - 2 + 2 \[Lambda] + \[Nu])) Subscript[\[ScriptCapitalC], n - 2][\[Nu], \[Lambda], z] && Element[n, Integers] && n > 0










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





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